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This paper presents a novel approach to the description and understanding of two-dimensional binary cellular automata with the Moore neighborhood that preserve the number of active cells. Such dynamical systems are known to successfully…
Regime shifts are quite common in complex systems like cell regulations, disease transmissions, ecosystems, marine ice instability, etc. Several statistical indicators known as early warning signals (EWS) have been theorized to anticipate…
A two parameter model for single lane car-following is introduced and its equilibrium and non-equilibrium properties are studied. Despite its simplicity, this model exhibits a rich phenomenology, analogous to that observed in real traffic,…
This paper demonstrates real-time short-term traffic flow prediction through distributed fiber-optic sensing (DFOS) and data assimilation with a stochastic cell-automata-based traffic model. Traffic congestion on expressways is a severe…
We determine the full distribution and moments of the first passage time for a wide class of stochastic search processes in the limit of frequent stochastic resetting. Our results apply to any system whose short-time behavior of the search…
We study the phase diagram and the critical behavior of a one-dimensional radius-1 two-state totalistic probabilistic cellular automaton having two absorbing states. This system exhibits a first-order phase transition between the fully…
We study a two-lane two-species exclusion process inspired by Lin et al. (C. Lin et al. J. Stat. Mech., 2011), that exhibits a non-equilibrium pulsing phase. Particles move on two parallel one-dimensional tracks, with one open and one…
We introduce a traffic flow model that incorporates clustering and passing. We obtain analytically the steady state characteristics of the flow from a Boltzmann-like equation. A single dimensionless parameter, R=c_0v_0t_0 with c_0 the…
We show techniques of analyzing complex dynamics of cellular automata (CA) with chaotic behaviour. CA are well known computational substrates for studying emergent collective behaviour, complexity, randomness and interaction between order…
By analyzing empirical time headway distributions of traffic flow, a hypothesis about the underlying stochastic process can be drawn. The results found lead to the assumption that the headways $T_i$ of individual vehicles follow a linear…
We modify the Nagel-Schreckenberg (NaSch) cellular automata model to study mixed-traffic dynamics. We focus on the interplay between passenger availability and bus-stopping constraints. Buses stop next to occupied cells of a discretized…
We develop a discrete Boltzmann-type model that uses dynamics in phase space to describe the behavior of traffic flows. Firstly, we model the traffic flow at mesoscopic scale using dynamics in phase space, which is considered as an…
Discrete dynamical systems can exhibit complex behaviour from the iterative application of straightforward local rules. A famous example are cellular automata whose global dynamics are notoriously challenging to analyze. To address this, we…
When suspended particles are pushed by liquid flow through a constricted channel they might either pass the bottleneck without trouble or encounter a permanent clog that will stop them forever. However, they may also flow intermittently…
Traffic on a circular road is described by dynamic programming equations associated to optimal control problems. By solving the equations analytically, we derive the relation between the average car density and the average car flow, known…
We consider the boundary crossing problem for time-homogeneous diffusions and general curvilinear boundaries. Bounds are derived for the approximation error of the one-sided (upper) boundary crossing probability when replacing the original…
Two different deterministic microscopic traffic flow models, which are in the context of the Kerner's there-phase traffic theory, are introduced. In an acceleration time delay model (ATD-model), different time delays in driver acceleration…
Stochastic systems characterised by a random driving in a form of the general stable noise are considered. The particle experiences long rests due to the traps the density of which is position-dependent and obeys a power-law form attributed…
Based on a detailed microscopic test scenario motivated by recent empirical studies of single-vehicle data, several cellular automaton models for traffic flow are compared. We find three levels of agreement with the empirical data: 1)…
We explore some aspects of phase transitions in cellular automata. We start recalling the standard formulation of statistical mechanics of discrete systems (Ising model), illustrating the Monte Carlo approach as Markov chains and stochastic…